•Topic:
Trig Propertes
Aim: how can we identify the reference angle given an angle terminating in other than quadrant I on the unit circle?
Aim: how can we identify the reference angle given an angle terminating in other than quadrant I on the unit circle?
•Do
Now: in a
45-45-90 right traingle, if
the hypoutenuse is
1, what is the length of the the two legs?
•
•Do
Now Solution
•Using
a 45-45-90 right triangle, if the hypotenuse is equal
to 1, what
is the length of the other two legs?
•Both
legs are equal (45-45-90)
•Leg =
1/√2 = √2/2
•
•Example
2
•Find the cos
of 300°
•
•Draw
a unit circle and label the radius (=1)
•
•Find
the reference angle and refer to CHART
•ALL
Students take Chemistry!
•Exact
value chart – save to notes
•Example
1: Finding the reference angle
•Find the exact value of sin 120°
•Step
1: Which quadrant? (II)
So, only sin is + ; all others are –
•Step
2: Find reference angle: 180 – 120 = 60° - always
makes angle with the x-axis!
• Step
3: identify sin 60° =
√3/2
(see prev chart)
•Step
4: synthesize steps 1-3.
•
•Therefore,
the sin
120°
= - √3/2
•Exit
slip
Point is
on the unit circle
whose center is the origin. If Θ is an angle in standard position whose
terminal ray passes through point A, what is the value of sin Θ?